The stochastic Fitzhugh–Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model
In this paper, we provide a complete mathematical construction for a stochastic leaky-integrate-and-fire model (LIF) mimicking the interspike interval (ISI) statistics of a stochastic FitzHugh–Nagumo neuron model (FHN) in the excitable regime, where the unique fixed point is stable. Under specific t...
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| Veröffentlicht in: | Journal of mathematical biology 2019-07, Vol.79 (2), p.509-532 |
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| creator | Yamakou, Marius E. Tran, Tat Dat Duc, Luu Hoang Jost, Jürgen |
| description | In this paper, we provide a complete mathematical construction for a stochastic leaky-integrate-and-fire model (LIF) mimicking the interspike interval (ISI) statistics of a stochastic FitzHugh–Nagumo neuron model (FHN) in the excitable regime, where the unique fixed point is stable. Under specific types of noises, we prove that there exists a global random attractor for the stochastic FHN system. The linearization method is then applied to estimate the firing time and to derive the associated radial equation representing a LIF equation. This result confirms the previous prediction in Ditlevsen and Greenwood (J Math Biol 67(2):239–259,
2013
) for the Morris-Lecar neuron model in the bistability regime consisting of a stable fixed point and a stable limit cycle. |
| doi_str_mv | 10.1007/s00285-019-01366-z |
| format | Article |
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2013
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2013
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2013
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| subjects | Applications of Mathematics Bistability Burning time Fixed points (mathematics) Mathematical and Computational Biology Mathematics Mathematics and Statistics Mimicry Stochasticity |
| title | The stochastic Fitzhugh–Nagumo neuron model in the excitable regime embeds a leaky integrate-and-fire model |
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